Mario buys a shirt for $28.95 and a pair of socks for $4.29. He gives the clerk at the store two 20 bills. How much change should Mario receive?
who contributed proof of complex functions to geometry
We can see here the proof of complex functions to geometry was contributed by the Norwegian mathematician Caspar Wessel.
What is complex function?A complex function is one that accepts a complex number as input and outputs another complex number. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain.
Wessel demonstrated in his article that complex functions and complex numbers may both be used to represent curves and points in the plane. This research was a significant advancement in the field of complex analysis and opened the path for its growth into a potent instrument for addressing geometric problems.
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Which of the following steps were applied to ABCD to obtain A'B'C'D'?
A. shifted 3 units right and 4 units up
B. shifted 3 units right and 2 units up
C. shifted 2 units right and 3 units up
D. shifted 2 units right and 4 units up
Part 2: Identify key features and graph a circle from general form.
I
Answer the following questions to determine the key features of the circle whose equation is shown and
then graph it.
x+y+12x-2y-12=0
a) Write the equation of the circle in standard form. (3 points)
b) What is the center of the circle? (1 point)
The equation of the circle is (x + 6)² + (y - 1)² = 7² and it's center is (-6, 1)
What is equation circleThe standard equation of a circle is given by:
(x - h)² + (y - k)² = r²
Where (h,k) is the coordinates of center of the circle and r is the radius.
In the given problem, the equation is;
x² + y² + 12x - 2y - 12 = 0
This can be rewritten as;
(x + 6)² + (y - 1)² = 7²
The center of the circle is (-6, 1) from the coordinates (h, k) of the equation of the circle.
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Adam wants to plant flowers in a triangular plot. He has three lengths of plastic edging that measures 8 feet, 15 feet, and 17 feet. Determine whether these pieces fit for a right triangle. Explain.
Using the Pythagorean triple formula the numbers 8, 15 and 17 are Pythagorean triple and as such will form a right-angle triangle.
What is Pythagorean triple?Pythagorean triples are x² = y² + z² where x, y and z are the three positive integers. These triples are represented as (x, y, z). Here, y is the perpendicular, z is the base and x is the hypotenuse of the right-angled triangle.
In this problem, to determine if the given numbers will form a right-angle triangle, we have to check if the numbers are Pythagorean triple.
In doing so, we would use the previous formula given as;
x² = y² + z²
In a Pythagorean triple, the largest side is the hypothenuse.
17² = 8² + 15²
289 = 64 + 225
289 = 289
The numbers are equal and they're Pythagorean triple.
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10. Mr. Brown bought a car for commuting to
work and completing errands. He found
that he traveled an average 1,100 miles per
month, with a standard of 100 miles. About 95% of the data lies in which interval
To determine the interval in which about 95% of the data lies, we can use the concept of standard deviation and the properties of the normal distribution.
Given that the average monthly mileage is 1,100 miles and the standard deviation is 100 miles, we can apply the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data. According to this rule:
- Approximately 68% of the data lies within one standard deviation of the mean.
- Approximately 95% of the data lies within two standard deviations of the mean.
- Approximately 99.7% of the data lies within three standard deviations of the mean.
Since the standard deviation is 100 miles, we can conclude that about 95% of the data lies within two standard deviations of the mean.
Therefore, the interval within which about 95% of the data lies is:
1,100 miles ± (2 * 100 miles) = 1,100 miles ± 200 miles
So, the interval is from 900 miles (1,100 miles - 200 miles) to 1,300 miles (1,100 miles + 200 miles).
d = 5t + 20
your answer is there so i'll be on my way, Have a nice day!!
a train of length 180 m approaches a tunnel of length 620 m. how long will it take the train to pass completely through the tunnel at a speed of 54 km per hour?
It will take the train 53.33 seconds to pass completely through the tunnel.
We have,
First, let's convert the speed from km/h to m/s:
54 km/h = 54000 m/3600 s = 15 m/s
We need to find the total distance the train travels, which is the sum of its length and the tunnel's length:
So,
distance = 180 m + 620 m = 800 m
Now we can use the formula:
time = distance/speed
time = 800 m / 15 m/s
time = 53.33 seconds
Therefore,
It will take the train 53.33 seconds to pass completely through the tunnel.
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Use the distributive property to remove the parentheses.
-5(- 6w + 2u -5)
The value of solution of the expression is,
⇒ - 5 (- 6w + 2u - 5)
Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
Expression is,
⇒ - 5 (- 6w + 2u - 5)
Now, By using distributive property we get;
⇒ - 5 (- 6w + 2u - 5)
⇒ - 5 × - 6w - 5 × 2u - 5 × - 5
⇒ 30w - 10u + 25
Thus, The value of solution of the expression is,
⇒ - 5 (- 6w + 2u - 5)
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What is the standard form of the line that passes through the points (-4, 6) and (0, -7)?
Ax+4y= -7
B
4x+y=-7
13x + 4y = -28
D-4x+y=-28
30960995
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-7}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-7 -6}{0 +4} \implies \cfrac{ -13 }{ 4 } \implies - \cfrac{13}{4}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{- \cfrac{13}{4}}(x-\stackrel{x_1}{(-4)}) \implies y -6 = - \cfrac{13}{4} ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{4}}{4(y-6)=4\left( - \cfrac{13}{4} ( x +4) \right)}\implies 4y-24=-13(x+4) \\\\\\ 4y-24=-13x-52\implies 13x+4y-24=-52\implies \boxed{13x+4y=-28}[/tex]
What value for the constant C makes Z=4 PLEASE HELP
The value of c that makes z = 4 an extraneous solution is c = -1.
We need to find the value of c that makes z = 4 an extraneous solution, which means that 4 is not a valid solution of the original equation but appears to be one when substituted into the equation.
First, we substitute z = 4 into the equation:
√ (3/2 x + 10) = cz + 8
√ (3/2 x + 10) = c(4) + 8
√(16) = 4c + 8
4 = 4c + 8
4c = -4
c = -1
Therefore, the value of c that makes z = 4 an extraneous solution is c = -1.
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Identify the domain and range for the graph:
0
O Domain: (-∞, ∞)
O Domain: (-∞, ∞)
O Domain: (∞, -∞)
Domain: (∞, -∞)
Range: (-4, ∞)
Range: (∞, - 4)
Range: (-4, ∞)
Range: (∞, - 4)
The options provided for the domain and range of the given graph are incorrect. The correct descriptions for the domain and range are as follows:
Domain: The domain represents the set of all possible input values, or the x-values, of the graph. Since no specific information is given about the graph or its equation, the domain is not specified. In this case, the correct answer is:
Domain: Not specified
Range: The range represents the set of all possible output values, or the y-values, of the graph. Similarly, without any specific information about the graph or its equation, the range is not specified. Therefore, the correct answer is:
Range: Not specified
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Help please (elementary statistics)
The sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.
To find the percentage of hospitals that provide at least some charity care, we need to use the given sample data.
(a) Using a calculator with mean and sample standard deviation keys, we can find the sample mean percentage x and the sample standard deviation S.
[tex]x = \frac{56.9 + 55.9 + 52.5 + 65.7 + 59.0 + 64.7 + 70.1 + 64.7 + 53.5 + 78.2}{10}\\\\ = 62.3% \\\\\\\\S = \sqrt{\frac{((56.9 - 62.3)^2 + (55.9 - 62.3)^2 + ... + (78.2 - 62.3)^2) }{ 9}}\\\\ = 8.08\%[/tex]
Therefore, the sample mean percentage x is 62.3% and the sample standard deviation S is 8.08%.
(b) To find a 90% confidence interval for the population average u of the percentage of hospitals providing at least some charity care, we can use the formula:
[tex]CI = x \pm z*(S/sqrtn)[/tex]
where CI is the confidence interval, x is the sample mean percentage, z is the z-score for the desired confidence level (90% in this case), S is the sample standard deviation, and n is the sample size (10 in this case).
From the z-table, the z-score for a 90% confidence level is 1.645.
Plugging in the values, we get:
CI = 62.3 ± 1.645*(8.08/sqrt(10)) = (55.5%, 69.1%)
Therefore, we can be 90% confident that the true population average percentage of hospitals providing at least some charity care is between 55.5% and 69.1%.
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Find the solution of the exponential equation
5^-x/16=5
in terms of logarithms, or correct to four decimal places.
x= ------------
here is the picture if you need it.
The solution of the equation [tex]\rm 5^{-x/16} = 5[/tex] will be negative 16.
Given that:
Equation, [tex]\rm 5^{-x/16} = 5[/tex]
In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
Take log on both sides, then we have
(-x / 16) log 5 = log 5
-x / 16 = 1
x = -16
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Building A is 165 feet tall and Building B is 210 feet tall. If the angle of depression from the top of Building B to the top of Building A is 52°, how far apart are the buildings?
help please
Help pls! ( Don’t mind this text)
The value of the expression 10 ÷ 40 using the long division method will be 0.25.
The expression is given below.
10 ÷ 40
Division means the separation of something into different parts, sharing of something among different people, places, etc.
The division is given below by the long division method. Then
40 ) 100 ( 0.25
- 80
200
- 200
0
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Marcela's grocery bills for three months were
$75, $87, and $25. To add the bills mentally,
Marcela thought:
"75 + 87 + 25 = 75 + 25 + 87"
What property did Marcela use?
Answer:
Marcela used the Associative Property of Addition.
Step-by-step explanation:
The Associative Property of Addition states that when adding three or more numbers, the grouping of the addends does not change the sum. In other words, no matter how the addends are grouped, the sum remains the same. More specifically:
For any three numbers a, b, and c, (a + b) + c = a + (b + c)
For example: (2 + 3) + 4 = 2 + (3 + 4) = 9
So, if Marcela used the Associative Property of Addition to add her grocery bills, she grouped the addends in a different order, but still arrived at the same sum.
What is the definition of withholding?
What function represents the same relationship
H(x)=-4+7
H(x) =-22x+1.75
H(x)=4x+1.75
H(x)=1.75x-4
The linear function that is modeled by the given table is:
y = -4x + 7
How to find the linear function represented by the table?A general linear function is written as:
y = ax + b
Where a is the slope and b is the y-intercept.
If we know two points on the line (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points on the table:
(-11, 51) and (-5.5, 29)
Then the slope is:
a = (29 - 51)/(-5.5 + 11)
a = -4
Then the linear function is:
y = -4x + b
We know that when x = -5.5, the value of y is 29
29 = -4*-5.5 + b
29 = 22 = b
29 - 22 = b
7 = b
The linear function is:
y = -4x + 7
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Suppose a star has a luminosity of 8.0×1026 watts
and an apparent brightness of 1.5×10−12 watt/m2
. How far away is it? Give your answer in both kilometers and light-years.
The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.
We have,
We can use the inverse square law to find the distance to the star:
Luminosity / (4π(distance)²) = Apparent brightness
Rearranging this formula to solve for the distance, we get:
distance = √(Luminosity / (4π (Apparent brightness)))
Plugging in the given values, we get:
distance = √(8.0 × 10^{26} / (4π (1.5 × 10^{-12}))
Simplifying this expression, we get:
distance = 3.04 × 10^{20} meters
Converting this distance to kilometers, we get:
distance = 3.04 × 10^{17} kilometers
To convert this distance to light-years, we divide by the speed of light in kilometers per year:
distance = (3.04 × 10^{17}) / (9.46 × 10^{12})
Simplifying this expression, we get:
distance = 32.2 light-years
Therefore,
The star is approximately 3.04×10^17 kilometers or 32.2 light-years away.
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find the area (exact)
The area of the figure is 24.28 cm²
What are composite shapes?Any figure that we can break and form more than one basic shape from is called a composite figure.
The composite figure can be broken into a right triangle, a rectangle and a semi circle.
area of triangle = 1/2 bh
= 1/2 × 4 × 3
= 2 × 3
= 6 cm²
area of the rectangle = l × w
= 3 × 4
= 12 cm²
area of the semi circle = 1/2 πr²
= 1/2 × 3.14 × 2²
= 3.14 × 2
= 6.28cm²
Therefore the area of the composite figure =
6 + 12 +6.28
= 24.28 cm
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Josiah ties together two strings. One string is 3 3/4 feet long. The other string is 1 1/2 yards long. The knot he makes to tie the strings subtracts 2 1/2 inches from the total length. Mark the length, in inches, of the two tied strings on the number line.
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
The length of the two tied strings on the number line would be between 96 and 97.
We first need to convert both the lengths of the strings to inches, since the knot's length is given in inches.
The first string is 3 3/4 feet long, which is equivalent to 45 inches (since 1 foot = 12 inches, and 3 3/4 feet = 45 inches).
The second string is 1 1/2 yards long, which is equivalent to 54 inches (since 1 yard = 36 inches, and 1 1/2 yards = 54 inches).
The total length of the two strings before the knot is tied is 45 inches + 54 inches = 99 inches.
Subtracting the length of the knot (2 1/2 inches) from the total length of the two strings gives us:
99 inches - 2 1/2 inches = 96 1/2 inches
Therefore, the length of the two tied strings on the number line would be between 96 and 97.
Since we know that the length is closer to 97 inches than 96 inches, we can mark the length at point 97 on the number line
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Cylinder A has radius r, height h, and a volume of 10% cubic units.
Cylinder B has twice the radius and twice the height.
B
Choose 1 answer:
What is the volume of cylinder B?
10 cubic units
20
cubic units
40% cubic units
2r
80% cubic units
2h
The volume of cylinder B include the following: D. 80π cubic units.
How to calculate the volume of a cylinder?In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Note: Radius of cylinder B = 2r
Height of cylinder B = 2h
By substituting the parameters, we have the following:
Volume of cylinder B = π × (2r)² × 2h
Volume of cylinder B = π × 4r² × 2h
Volume of cylinder B = π × 8r²h
Volume of cylinder B = 8 × πr²h
Volume of cylinder B = 8 × 10π
Volume of cylinder B = 80π cubic units.
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mr.james is teaching his studens about the volume of rectangular prisms.He has various rectangular prisms with a height of 6 inches
The equation that can be used to calculate the base areas of the rectangular prisms is B = V/6
Calculating the equation can be used to find B, the area of the base with volume VFrom the question, we have the following parameters that can be used in our computation:
Volume of rectangular prisms
The volume of rectangular prisms is calculated as
V = Bh
Where
B = Base area
h = height
Given that
h = 6 inches,
We have
V = B * 6
Divide both sides by 6
B = V/6
This means that the the equation to calculate the base areas is B = V/6
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Complete question
Mr. James is teaching his studens about the volume of rectangular prisms.He has various rectangular prisms with a height of 6 inches
Which equation can be used to find B, the area of the base with volume V
find the value of x such that line L and M are parrle
Answer:
3x+10+5x+18=180
8x+28=180
8x= 152
x=19
Pls help me I will mark the brainliest
The most specific correct name for this figure is a trapezoid.
A trapezoid is a quadrilateral with only one pair of parallel sides. >>>This figure is a trapezoid.
An isosceles trapezoid is a trapezoid in which the top and bottom sides are parallel, while the remaining two non-parallel sides have the same length. >>> this figure is not an isosceles trapezoid.
A parallelogram has opposite sides parallel. >>> This figure is not a parallelogram.
A quadrilateral is a four-sided polygon, having four edges and four corners. >>>This figure is a quadrilateral.
-3*10^2t=-28 Solve the equation for
t
Express the solution as a logarithm in base-
10
The solution for t is t = log(28/3) / 2, the Logarithm in base-10.
The equation -3 * 10^(2t) = -28 for t, the exponential term and then take the logarithm of both sides. Let's go through the steps:
Step 1: Divide both sides of the equation by -3:
(10^(2t)) = -28 / -3
Step 2: Simplify the right-hand side:
(10^(2t)) = 28/3
Step 3: Take the logarithm of both sides using base-10 logarithm (log):
log(10^(2t)) = log(28/3)
Step 4: Apply the power rule of logarithms to bring down the exponent:
2t * log(10) = log(28/3)
Step 5: Since log(10) = 1, we have:
2t = log(28/3)
Step 6: Divide both sides of the equation by 2:
t = log(28/3) / 2
Therefore, the solution for t is t = log(28/3) / 2, where log represents the logarithm in base-10.
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Lacey's mom makes her a birthday cake in the shape of an "L" . Lacey loves frosting, so her mom covers the entire outside of the cake in frosting, even the bottom of the cake. How much space does Lacey's mom cover in frosting?
Answer:
220 in.²
Step-by-step explanation:
top face - rectangle: A = LW = 4 in. × 2 in. = 8 in.²
bottom face - rectangle: A = LW = 9 in. × 2 in. = 18 in.²
left face - rectangle: A = LW = 12 in. × 2 in. = 24 in.²
right upper face - rectangle: A = LW = 8 in. × 2 in. = 16 in.²
right lower face - rectangle: A = LW = 4 in. × 2 in. = 8 in.²
middle horizontal face - rectangle: A = LW = (9 - 4) in. × 2 in. = 10 in.²
front L-shaped face - 2 rectangles: A = (12 × 4 + 5 × 4) in.² = 68 in.²
back L-shaped face - same as front L-shaped face: A = 68 in.²
total surface area = (8 + 18 + 24 + 16 + 8 + 10 + 68 + 68) in.²
total surface area = 220 in.²
What is the square root of 35*35*35?
Answer:
Step-by-step explanation:
7247.1977343
The square root of (35 x 35 x 35) is approximately 207.57.
The square root of (35 x 35 x 35) can be found by simplifying the expression under the radical sign:
√(35 x 35 x 35) = √(35³)
On simplifying 35³ to get:
√(35³) = √(42,875) ≈ 207.57
Therefore, the square root of (35 x 35 x 35) is approximately 207.57.
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The equation a(s) = 37.5s - 1.5s2 models the function
represented in the table. Fill in the blank to complete the
restricted domain of the function. D = {0 ≤s ≤
The restricted domain of the function is 0≤s≤25
The equation is a(s) = 37.5s - 1.5s² models the function represented in the table
a(s) = s(37.5 - 1.5s)
The critical points are s=0 or
37.5 - 1.5s
37.5 = 1.5s
s=25
As area can not be negative, the area should be positive
s< 0 and s>25
Therefore, restricted domain is 0≤s≤25
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can someone help me with this question please?
The value of the missing angle x is: 38°
How to find the angle of the parallelogram?We know that the sum of angles in a triangle is 180 degrees and as such:
∠DAE = 180 - (82 + 68)
∠DAE = 30°
Now, we know that alternate angles are congruent. Thus:
∠DAE ≅ ∠ADC = 30°
Opposite angles of a parallelogram are equal (or congruent) Consecutive angles are supplementary angles to each other (that means they add up to 180 degrees).
Thus:
∠BAE = ∠BDE = 82 + 30
= 112°
Thus:
∠ABC = ∠ACB = 68°
Thus:
∠BAC = 180 - 2(68)
∠BAC = 44°
Thus:
x = 112 - (44 + 30)
x = 112 - 74
x = 38°
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